Universal C*-algebra of real rank zero

Abstract

It is well-known that every commutative separable unital C*-algebra of real rank zero is a quotient of the C*-algebra of all compex continous functions defined on the Cantor cube. We prove a non-commutative version of this result by showing that the class of all separable unital C*-algebras of real rank zero concides with the class of quotients of a certain separable unital C*-algebra of real-rank zero.